Is this quadrilateral a parallelogram, rectangle, rhombus or square? Which facts are enough?

Answer Key - Grade 10 Math Worksheet

Circle the best answer, or write your answer on the line.

2. 1.

   Esme has four cards, each with facts about DFGH. Which card proves that DFGH is a parallelogram?

   • DF ∥ HG and DF = HG
   • DF = DH and GF = GH
   • DF = HG only
   • DF ∥ HG and FG = DH
3. 2.

   Kira has four cards, each with facts about DFGH. Which card proves that DFGH is a parallelogram?

   Use the picture in question 1.

   • ∠F = ∠H only
   • DF ∥ HG, ∠D = ∠F and ∠G = ∠H
   • DQ = QG and FQ = QH
   • FG = DH only
4. 3.

   Luz has four cards, each with facts about DFGH. Which card proves that DFGH is a parallelogram?

   Use the picture in question 1.

   • DF = HG and FG = DH
   • DF ∥ HG and DG = FH
   • DF ∥ HG only
   • DG ⊥ FH and FQ = QH
5. 4.

   Milo knows DFGH is a parallelogram. Its diagonals are equal: DG = FH. Which name fits DFGH best?

   • Rhombus
   • Just a parallelogram
   • Rectangle
   • Square
6. 5.

   Pia knows DFGH is a parallelogram. DF = FG, and m∠D = 90°. Which name fits DFGH best?

   • Rhombus
   • Square
   • Rectangle
   • Just a parallelogram
7. 6.

   Ren knows DFGH is a parallelogram. Its diagonals are equal and cross at right angles. Which name fits DFGH best?

   • Just a parallelogram
   • Square
   • Rectangle
   • Rhombus
8. 7.

   Tala's picture frame DFGH has DF ∥ HG. m∠D = (3x − 5)° and m∠F = (2x + 15)°. What value of x makes DH ∥ FG, so DFGH is a parallelogram?

   34
9. 8.

   Zee's garden bed DFGH has DF ∥ HG. m∠D = (4x − 8)° and m∠F = (2x + 20)°. What value of x makes DH ∥ FG, so DFGH is a parallelogram?

   28
10. 9.

    Ari's window DFGH has DF ∥ HG. m∠D = (5x − 15)° and m∠F = (3x + 11)°. What value of x makes DH ∥ FG, so DFGH is a parallelogram?

    23
11. 10.

    Bo's tile DFGH has DF ∥ HG. m∠D = (2x + 14)° and m∠F = (4x − 8)°. What value of x makes DH ∥ FG, so DFGH is a parallelogram?

    29